Unlike the resistor, which dissipates energy in the form of heat, the ideal capacitor does not loose its energy. We have also seen that the simplest form of a capacitor is two parallel conducting metal plates which are separated by an insulating material, such as air, mica, paper, ceramic, etc, and called the dielectric through a distance, “d”.
Capacitors store energy as a result of their ability to store charge with the amount of charge stored on a capacitor depending on the voltage, V applied across its plates, and the greater the voltage, the more charge will be stored by the capacitor as: Q ∞ V.
Also, a capacitor has a constant of proportionality, called capacitance, symbol C, which represents the capacitor’s ability or capacity to store an electrical charge with the amount of charge depending on a capacitor capacitance value as: Q ∞ C.
Then we can see that there is a relationship between the charge, Q, voltage V and capacitance C, and the larger the capacitance, the higher is the amount of charge stored on a capacitor for the same amount of voltage and we can define this relationship for a capacitor as being:
Charge on a Capacitor
Where: Q (Charge, in Coulombs) = C (Capacitance, in Farads) times V (Voltage, in Volts)
The unit of capacitance is the coulomb/volt, which is also called the Farad (F) [named after M. Faraday] with one farad being defined as the capacitance of a capacitor, which requires a charge of 1 coulomb to establish a potential difference of 1 volt between its two plates.
But a conventional one farad capacitor would be very large for most practical electronic applications, hence much smaller units like the microfarad (μF), nanofarad (nF) and picofarad (pF) are commonly used where:
- Microfarad (μF) 1μF = 1/1,000,000 = 0.000001 = 10-6 F
- Nanofarad (nF) 1nF = 1/1,000,000,000 = 0.000000001 = 10-9 F
- Picofarad (pF) 1pF = 1/1,000,000,000,000 = 0.000000000001 = 10-12 F
However, there is another type of capacitor available, called an Ultracapacitor or Supercapacitor which can provide values from a few milli-farads (mF) to ten’s of farads of capacitance in a very small size allowing for much more electrical energy to be stored between their plates.
In our tutorial about Capacitance and Charge we saw that the energy stored in a capacitor is given by the equation:
Where: E is the energy stored in the electric field in joules, V is the potential difference across the plates and C is the capacitance of the capacitor in farads and defined as:
Where: ε is the permittivity of the material between the plates, A is the area of the plates, and d is the separation of the plates.
Ultracapacitors are another type of capacitor which is constructed to have a large conductive plate, called an electrode, surface area (A) as well as a very small distance (d) between them. Unlike conventional capacitors that use a solid and dry dielectric material such as Teflon, Polyethylene, Paper, etc, the ultracapacitor uses a liquid or wet electrolyte between its electrodes making it more of an electrochemical device similar to an electrolytic capacitor.
Although an ultracapacitor is a type of electrochemical device, no chemical reactions are involved in the storing of its electrical energy. This means that the ultra-capacitor remains effectively an electrostatic device storing its electrical energy in the form of an electric field between its two conducting electrodes as shown.
The double sided coated electrodes are made from graphite carbon in the form of activated conductive carbon, carbon nanotubes or carbon gels. A porous paper membrane called a separator keeps the electrodes apart but allows positive ion to pass through while blocking the larger electrons. Both the paper separator and carbon electrodes are impregnated with the liquid electrolyte with an aluminium foil used in between the two to act as the current collector making electrical connection to the ultracapacitors solder tabs.
The double layer construction of the carbon electrodes and separator may be very thin but their effective surface area into the thousands of meters squared when coiled up together. Then in order to increase the capacitance of an ultra-capacitor, it is obvious that we need to increase the contact surface area, A (in m2) without increasing the capacitors physical size, or use a special type of electrolyte to increase the available positive ions to increase conductivity.
Then ultra-capacitors make excellent energy storage devices because of their high values of capacitance up into the hundreds of farads, due to the very small distance d or separation of their plates and the electrodes high surface area A for the formation on the surface of a layer of electrolytic ions forming a double layer. This construction effectively creates two capacitors, one at each carbon electrode, giving the ultracapacitor the secondary name of “double layer capacitor” forming two capacitors in series.
However, the problem with this small size is that the voltage across the capacitor can only be very low as the rated voltage of the ultra-capacitor cell is determined mainly by the decomposition voltage of the electrolyte. Then a typical capacitor cell has a working voltage of between 1 to 3 volts, depending on the electrolyte used, which can limit the amount of electrical energy it can store.
In order to store charge at a reasonable voltage ultracapacitors have to be connected in series. Unlike electrolytic and electrostatic capacitors, ultra-capacitors are characterized by there low terminal voltage. In order to increase there rated terminal voltage to tens of volts, ultracapacitor cells must be connected in series, or in parallel to achieve higher capacitance values as shown.
Increasing An Ultracapacitors Value
Where: VCELL is the voltage of one cell, and CCELL is the capacitance of one cell.
As the voltage of each capacitor cell is about 3.0 volts, connecting more capacitor cells together in series will increase the voltage. While connecting more capacitor cells in parallel will increase its capacitance. Then we can define the total voltage and total capacitance of a ultracapacitor bank as:
Where: M is the number of columns and N is the number of rows. Note also that like batteries, ultracapacitor and supercapacitors have a defined polarity with the positive terminal marked on the capacitor body.
Ultracapacitor Example No1
A 5.5 volt, 1.5 farad ultracapacitor is required as an energy storage backup device for an electronic circuit. If the ultracapacitor is to be made from individual 2.75v, 0.5F cells, calculate the number of cells required and the layout of the array.
The array will therefore have two capacitor cells of 2.75v each connected in series to provide the required 5.5v.
Then the array will have a total of six individual columns, consisting of two rows of six thereby forming an ultracapacitor with a 6 x 2 array as shown.
6×2 Ultracapacitor Array
As with all capacitors, an ultracapacitor is a energy storage device. Electrical energy is stored as charge in the electric field between its plates and as a result of this stored energy, a potential difference, that is a voltage, exists between the two plates. During charging (current flowing through the ultracapacitor from the connected supply), electrical energy is stored between its plates.
Once the ultracapacitor is charged, current stops flowing from the supply and the ultracapacitors terminal voltage is equal to the voltage of the supply. As a result, a charged ultracapacitor will store this electrical energy even when removed from the voltage supply until it is needed acting as an energy storage device.
When discharging (current flowing out), the ultracapacitor changes this stored energy into electrical energy to supply the connected load. Then an ultracapacitor does not consume any energy itself but instead will store and release electrical energy as required with the amount of energy stored in the ultracapacitor being in proportion to the capacitance value of the capacitor.
As previously mentioned, the amount of energy stored is proportional to the capacitance C and the square of the voltage V across its terminals giving.
Where: E is the energy stored in joules. Then for our ultracapacitor example above, the amount of energy stored by the array is given as:
Then the maximum amount of energy that can be stored by our ultracapacitor is 22.7 joules, which was originally supplied by the 5.5 volt charging supply. This stored energy remains available as charge in the electrolyte dielectric and when connected to a load, the ultracapacitors entire 22.69 joules of energy is made available as an electric current. Obviously, when the ultracapacitor is fully discharged, the stored energy is zero.
Then we can see that an ideal ultracapacitor would not consume or dissipate energy, but instead take power from an external charging circuit to store energy in its electrolyte field and then return this stored energy when delivering power to a load.
In our simple example above, the energy stored by the ultracapacitor was about 23 joules, but with large capacitance values and higher voltage ratings, the energy density of ultracapacitors can be very large making them ideal as energy storage devices.
In fact, ultracapacitors with ratings into the thousands of farads and hundreds of volts are now being used in hybrid electric vehicles (including Formula 1) as solid state energy storage devices for regenerative braking systems as they can quickly giving out and receiving energy during braking and accelerating afterwards. Ultra and super-capacitors are also used in renewable energy systems to replace lead acid batteries.
We have seen that an ultracapacitor is an electrochemical device consisting of two porous electrodes, usually made up of activated carbon immersed in an electrolyte solution that stores charge electrostatically. This arrangement effectively creates two capacitors, one at each carbon electrode, connected in series.
The ultracapacitor is available with capacitances in the hundreds of farads all within a very small physical size and can achieve much higher power density than batteries. However, the voltage rating of an ultracapacitor is usually less than about 3 volts so several capacitors have to be connected in series and parallel combinations to provide any useful voltage.
Ultracapacitors can be used as energy storage devices similar to a battery, and in fact are classed as an ultracapacitor battery. But unlike a battery, ultracapacitors can achieve much higher power densities over a shorter time duration. Also, ultracapacitors are now used in many hybrid petrol vehicles as well as fuel cell driven electric vehicles due to their ability to discharge high voltages quickly and then be recharged once again ready for the next cycle. By using ultracapacitors along with conventional fuel cells and automotive batteries, peak power demands and transient variations in load conditions can be controlled much more efectively.